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When the power source for a circuit is oscillatory, meaning
the voltage changes periodically with time, we call these
circuits, AC circuits.
In a circuit diagram, an AC power source is denoted by
The simplest AC circuits is one where we have an AC power
s

We
have considered an AC circuits where an AC voltage source is
connected in series with a resistor, an inductor, and a capacitor, such a
circuit exhibit resonance behavior. We can consider a RLC series
circuit as a band pass filter if we consider the vo

Lets consider an AC circuits where an AC voltage source is
connected in series with a resistor, an inductor, and a
capacitor.
What do you think the current in the circuit would look
like as a function of time?
We will analyze this circuit using phasor dia

is the equivalent capacitance of this series circuit.
In
general, for N capacitors in a series circuit
is the equivalent capacitance of the series circuit.
Another way that multiple capacitors can be connected
together in a circuit is for them to be in p

We found earlier that for a parallel-plate capacitor, we have
and
and
d
Equipotential
Lines
The electric potential relative
to the negative plate, increases
linearly with distance from the
negative plate.
The electric field is constant
and points from th

The set up of a transformer
gives us the relationship
which implies that the current flowing through
the secondary coil somehow influence the
current flow in the primary coil.
Another way to understand the relationship
is to ask,
How does the primary coil

We
have considered an AC circuits where an AC voltage source is
connected in series with a resistor, an inductor, and a capacitor, such a
circuit exhibit resonance behavior. We can consider a RLC series
circuit as a band pass filter if we consider the vo

Simple capacitor
example revisited
The spacing between the plates of a 1F capacitor is
0.05 mm. The plates are circular and equal in size. We
filled the space between the plates with titanium
dioxide which has a dielectric constant of .
What is the surfa

When a wire is connected to a source of electric
potential difference like a battery or a charged
capacitor,
What do you think happen?
When a wire is connected to a source of electric potential difference
like a battery or a charged capacitor, Two things

What happen to the electric energy of the charge as it goes
through the resistor?
+
_
You can picture the resistor as a region in the circuit where
the charge experiences a lot of collision as it falls to a lower
electric potential. Thus energy is loss to

Lets determine the mathematical relationship between
voltage and current in a circuit.
As stated earlier, the acceleration of a charge particle in a
circuit is determined by the electric field in the wire:
If we assume the moving charges in a circuit are

For series circuits:
For parallel circuits:
In general,
and
Ladder Example
Find the equivalent resistance for this circuit.
Ladder Example
Find the equivalent resistance for this circuit.
How should we start?
We should start at the end.
Ladder Example
Fi

Lets analyze a circuit with a battery, a
capacitor, a resistor, and a switch.
A Switch
B
When we turn the switch to position A,
the circuit becomes
B
Right after the switch is turn to position A,
charges will flow from the battery through the
resistor, to

Applying the matrix method to find the currents in the
circuit,
We found
=0.091 A
= 0.0455 A
= 0.0303 A
= 0.01515 A
=+= 0.0455 A
We could have also solved this problem by first simplifying the circuit,
and thinking through how the current will move throug

Quiz problem 4.
Two similar conducting sphere are separated by a distance d. One
sphere carries charge +Q and the other carries Q. They each feel an
attractive force F. If one third of the charge on the negative sphere is
transferred to the positive spher

For points very close to a disk,
Here,
k is the electrostatic constant, and is a constant for a given
disk.
P
d
The result
tells us that for points close to a disk, the electric field is a
constant independent of distance.
This result is valid as long as

Electric field on a charged ring central axis
Take a thin ring (no thickness) of radius R with uniformly
distributed charge +Q. Find the electric field at point P that
is a distance d along the central axis of the ring.
P
d
Electric field on a charged rin

Amperes Law is
Here,
is the sum of the magnetic field component that is parallel to a closed
curve.
is the net current enclosed be the closed curve.
For an infinitely long, thin, straight wire carrying a
constant current we found that using Biot-Savarts

Faradays law of induction states that
Nature will always generate an to oppose changes in the
magnetic flux through the area enclosed by a conducting
loop.
Which can be written mathematically as
Lets consider a complementary situation to the one we examin

Lets consider a conductor of length that moves with
velocity, through a uniform magnetic field, .
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
into the page
What will the charges inside the conductor do as the
conductor moves through the magnetic field?
What will

From
applying Faradays and Ampere-Maxwells Laws to a time varying
electric and magnetic field, we got
and
We can combine these two equations to get,
and
These two equations describe the propagation of electromagnetic waves
and
The solution of these two e

For an arbitrary shaped enclosure with a light source inside,
if we add up all the intensity at every points on the surface of the
enclosure and multiple that by the total surface area of the enclosure,
then we will get the total power output of the light

Faradays law of induction states that
Nature will always generate an to oppose changes in the
magnetic flux through the area enclosed by a conducting
loop.
Which can be written mathematically as
What exactly is this ?
In a DC circuit, the is the electric

What is the goal of learning
electrostatics?
What is the goal of learning
electrostatics?
The goal is to be able to predict the force on an electric
charge if we place it in a region of space.
If we can systematically design what force is apply to
an elec

PHYS 102
First Day Info
Welcome
Before starting with the material, there are
some organizational things we have to discuss
These slides will be posted in owlspace, you
dont need to write this down.
Syllabus
It is important that you read the syllabus
T

Electric field outside a spherical ball example
Suppose you have a spherical ball of charge, Q, (Not a point
charge). What is outside this ball?
Electric field outside a spherical ball example
We can use Gauss Law to find outside this ball of charge by
im

The equal sign in the equation does not imply causation but
correlation.
A changing magnetic flux DOES NOT cause a circulating
electric field to appear.
The equation tells us that a changing magnetic flux is
always ACCOMPANIED by a circulating electric f

For
this circuit
, the current through the circuit is given by
,and the electric potential difference across the inductor is
given by
Here, is the electrical potential difference that was used to energize
the inductor, and .
So, the inductor acts like a

For
an inductor
and
so,
Also,
For
a Capacitor
and
so,
Also,
When an inductor is first connected to a DC power supply,
the back across the inductor is at its maximum value, and
the current through the inductor is zero, so the magnetic
field in the inducto